Non-Newtonian Mechanics. 151 



where c is the velocity of light and k is put equal to 

 1 



By the obvious differentiations and substitutions, Einstein 

 lias obtained the further equations : 



dt 



dt 



-(!-?> •'■ W 



k <=JLJL (6) 



VX V J 



*'=-^j, ' (8) 



VX v 



-'-' &c. 



where for simplicity we have put 



dx _ . dx J _ 



di-~ tV > ~dt'~ x - 



If, for an observer in system S, a point is moving with the 

 velocity (x, y, z) its velocity (x' f y', z'), as seen by an ob- 

 server in system S', is given by equations (6), (7), and (8). 

 It is interesting to note that if to one observer a particle 

 appears to have a constant velocity, that is not to be acted 

 on by any force, it appears so to any other observer who is 

 in uniform motion. 



By further differentiation and simplification it is possible 

 to obtain from equations (6), (7), and (8) three new equations 

 for transforming measurements of acceleration from system 

 S to S', viz. :— 



*=(l-S)-V«*. (9) 



y'=(l-J)"%- 2 y+^^(l-f) ~V 2 *, • (10) 



In contrast to the relation holding for the case of uniform 

 velocity, it may be pointed out in connexion with the above 



